Is there another coincidence problem at the reionization epoch?

Understand

The cosmological coincidences between the matter and radiation energy densities at recombination as well as between the densities of matter and the cosmological constant at present time are well known.

• We point out that moreover the third intersection between the energy densities of radiation and the cosmological constant coincides with the reionization epoch.
• To quantify the statistical relevance of this concurrence, we compute the Bayes factor between the concordance cosmology with free Thomson scattering optical depth and a model for which this parameter is inferred from imposing a match between the time of density equality and the epoch of reionization.
• This is to characterize the potential explanatory gain if one were to find a parameter-free physical connection.